curve #332

y² + xy + y = x³ + x² − 87896211291767885909452033582x + 10032036623674987328062504411246312614248555

a-invariants: [1, 1, 1, -87896211291767885909452033582, 10032036623674987328062504411246312614248555]
rank (lower bound): ≥ 19
torsion subgroup: trivial
conductor (N): 11000203474134513163114551624790609684216808458508386590177281881926
naive height: 211.5519
Faltings height: 15.3467
discriminant (Δ): -17167909180637480883395526936559530872769554325924464584539224547488746121889587183616
primes of bad reduction: 2, 3, 7, 17, 19, 37, 61, 71, 73, 69316422129706338470662069609749205202946553954322684531
regulator: 1849713008892069162.162532891599780163265102933993712449046864025910208639975
submitted by: 7fff-zip
submitted at: 2026-08-24 19:17:54 UTC
last updated: 2026-08-24 19:17:54 UTC

Witness: 19 independent points

(22379054239159361, -3347531525037033343948377)
(3646730481788423, -219513249242184999428259)
(137922453018922928609/46225, -1612058146940998846331031767007/9938375)
(13210141533447499/9, -1489475020709247134433845/27)
(-20645141097552823/1849, 263839353057070445828104437/79507)
(58101106471791461/2401, 331077574868547035277880935/117649)
(1416391468490569/9, 8410613058716250897821/27)
(4242297178834205072017/25411681, 13481525034579180739750184946759/128100283921)
(2686808745548745585959/15856324, 3734203274231222545781528180805/63139882168)
(1888414406611431087089/10975969, 1774095388506234845272904301831/36363385297)
(173995554471825, 78146159707741567255)
(6273773583732509/25, 242975691725347075655067/125)
(109656060388391608012625/424813321, 18661640351301329963039721473528805/8755827359131)
(3037767624896724125/24649, 4005752138987940151799504415/3869893)
(591163905736875089833/4076361, 4764648893991205856798967456845/8230172859)
(33321364225744085475105/25694761, 5935795661282938457835449233218755/130246743509)
(152431711876145, 419144946573253064439)
(-75536487613842984167/692224, 2465361180213569582344333063779/575930368)
(-7068944142404731327/196249, 315279922533780173756729954853/86938307)

Commentary

New in this search: Mestre quartic family with roots [0,115,206,234,731,784], T=15123/14. 19 independent rational points certified exactly by Cremona-Brumer quadratic characters; quartic point box [10000000,10000].

last edited by 7fff-zip at 2026-08-24 19:17:54 UTC · history